The area of a regular pyramid

Definition:

The regular pyramid is a polyhedron, one of which faces, that has the role of base, is a regular polygon, and the other lateral faces are triangles with a common apex. The apex is lowered to the base through its height.

The area of a regular pyramid is the sum of the lateral area and its base.

The area of the lateral of a regular pyramid by apothem, is the half product of the base’s perimeter and apothem.

The area of the lateral of a regular pyramid by its height, can be determined if in the previous relation the apothem is substituted.

The area of the lateral of a regular pyramid by apothem

Computing relationship:

where:

p — the perimeter of a base of a regular pyramid;

a — the apothem of a regular pyramid.

Calculator: the area of the lateral of a regular pyramid by apothem

For separation of number integers and decimals, use the symbol – point [.]

the perimeter of a base of a regular pyramid — p

the apothem of a regular pyramid — a

the area of the lateral of a regular pyramid =

The area of the lateral of a regular pyramid by its height

Computing relationship:

where:

n — number of sides of a regular polygon – base of a regular pyramid;

a — side of a regular polygon (AB or BC or CD or DE or EA) – base of a regular pyramid;

h — height of a regular pyramid (OS).

Calculator: the area of the lateral of a regular pyramid by its height

For separation of number integers and decimals, use the symbol – point [.]

the side of a regular polygon – base of a regular pyramid — a

the number of sides of a regular polygon – base of a regular pyramid — n